Conventional wisdom suggests that Progressive Rock, or "Prog-Rock" - bands that do not regularly get their songs played on the radio - write and record songs that are longer than other "Hard Rock" bands that receive regular radio airplay. The reason being that "prog-rock bands songs are played less often than "hardrock bands songs, since song-length is not limited to fit in radio-station format and allow for commercials between air- play. To test this claim, a statistics professor randomly selected songs from two of his playlists on his iPod, the "ProgRock" playlist and the "Hard Rock" playlist, and recorded the length of each song in minutes. The data is found in the accompanying data file. Use a = 0.05 for all calculations. Download .csv file Let μPR represent the mean length of songs in the professor's "ProgRock" playlist, and be the mean length of songs in his "HardRock" playlist. (a) Construct the most appropriate statistical hypotheses that will test this professor's claim. O A. Ho: PR-PHR 20 ⒸB. Ho: APR-PHR 20 OC. Ho: PR-PHR=0 O D. Ho: PPR-PHR>0 O E. Ho: PPR-PHR=0 HAPPR-PHR <0 HAPPR-PHR>0 HAPPR-PHR > 0 HAPPR-PHR <0 HAPPR-PHR <0 (b) Using technology available to you, does there appear to be a difference in the variation in song-length between progressive rock bands and heavy rock bands? O A. There appears to be equal variation in the song-length when comparing progressive rock bands and heavy rock bands. ⒸB. There appears to be less variation in the song-length of progressive rock bands when compared to heavy rock bands. O C. There appears to be more variation in the song-length of progressive rock bands when compared to heavy rock bands. O D. There appears to be unequal variation in the song-length when comparing progressive bands to heavy rock bands. (c) Report the p-value of the test you ran in (b) use at least three decimals in your answer. P-value= (d) Test the statistical hypotheses in (a) by carrying out the appropriate statistical test. Find the value of the test statistic for this test, use Test Statistic = (e) Determine the P-value of your statistical test in part (d), and report it to at least three decimal places. P= (f) Determine the appropriate degrees of freedom for the test in part (d). Use at least 3 digits after the decimal. DF= (g) Using ana of 5%, this data suggest that the null hypothesis should ? ✓Progressive rock songs are ? least two decimals in your answer. ✓when compared to the length of heavy rock songs.